Predicting Octane of Gasoline Blendstocks

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The present invention relates to a processes for blending a finished hydrocarbon fuel such as gasoline utilizing a generalized blend model that maintains product quality over time while maximizing profit and meeting all government specifications for the finished fuel.

Product blending operations significantly impact refinery profitability and profit suffers when blended fuel products are produced that exceed government specifications for quality. Product quality giveaway refers to the lost profit opportunity that is realized by producing fuels possessing properties (e.g., octane number or volatility) that significantly surpass the government mandated specifications. Excess fuel octane represents a significant percentage of lost profit opportunity for petroleum refineries and therefore remains an opportunity to capture significant value.

Fuel blend models are used to control commercial gasoline blending and thus are integral to minimizing excess fuel octane and maximizing profit. Chemometrics has been integrated into fuel blend models by correlating one or more physical or chemical properties of a fuel blend component with its octane rating. Refineries often maintain chemometric models for different fuel grades, resulting in a collection of models for each fuel grade, each model tailored for a specific season (or ambient temperature range) that occurs throughout the year. While tailoring models to specific fuel grades can drive optimal blending and minimize fuel octane excess, maintaining the models is labor intensive, especially around transition periods between blend models when blend models often perform sub-optimally. This approach also often results in an excess of blend models at a given refinery because new models may be developed for slight changes in feed composition and/or chemistry. A large number of models makes model maintenance labor-intensive and expensive and the performance of these models often deteriorates over time. What is needed are fewer, more generalized blend models that are more broadly applicable while consistently minimizing excess octane rating of produced transportation fuel products.

Some embodiments comprise a process for blending a finished fuel, comprising: a) analyzing a first collection of liquid hydrocarbon samples comprising multiple finished gasolines by near-infrared spectroscopy to produce a first spectral database that comprises at least one near-infrared spectrum for each finished fuel and analyzing a second collection of liquid hydrocarbon samples comprising multiple gasoline blend component streams by near-infrared spectroscopy to produce a second spectral database that comprises at least one near-infrared spectrum for each fuel blend component stream, where each near-infrared spectrum comprises spectral data comprising multiple data points; b) identifying research octane spectral features in each spectral database that comprise a subset of the spectral data that correlates with research octane number for each of the first collection and the second collection and identifying motor octane spectral features in each spectral database that comprise a subset of the spectral data that correlates with motor octane number for each of the first collection and the second collection, where the identifying results from correlating the spectral data for each member of each collection with an empirically-derived octane number for that member that is selected from road octane number and motor octane number utilizing a machine learning algorithm; c) selecting a first subset of the spectral features that best correlates with the research octane number to produce a research octane spectral features; d) selecting a second subset of the spectral features that best correlates with the motor octane number to produce a motor octane spectral features database; e) producing a first octane model that predicts research octane number for one or more gasoline blend component streams by training a first octane model algorithm on the research octane spectral features database; f) producing a second octane model that predicts motor octane number for one or more gasoline blend component streams by training a second octane model algorithm on the motor octane spectral features database; g) calculating a volumetric blend ratio comprising at least one gasoline blend component to produce a finished gasoline that meets government specifications for anti-knock index while simultaneously minimizing the difference between the anti-knock index of the finished gasoline and government specifications for minimum anti-knock index, where the calculating comprises using the first blend model and to predict the research octane number and the second blend model to predict the motor octane number for each gasoline blend component that is utilized to produce the finished gasoline.

Some embodiments additionally comprise mathematically converting the spectral data from part a) to wavelets coefficients data prior to the identifying of part b).

In some embodiments, the mathematically converting comprises decomposing the spectral data obtained from each near infrared spectrum into approximation and detail components using a mother wavelet selected from the Symlet, Haar, and Coiflets families of mother wavelets.

Some embodiments additionally comprise pre-processing the spectral data within the spectral database to produce corrected spectral data, where the pre-processing includes one or more of baseline correction, manual curation of the spectral data to remove data outliers and standardizing by removing the mean and scaling to unit variance.

In some embodiments, producing the finished gasoline is performed by a programmable logic controller, where the programmable logic controller comprises at least one processor that executes programming that incorporates the first octane model and the second octane model, where the programmable logic controller dynamically adjusts volumetric blend ratio of the multiple gasoline blend components based at least in part upon a research octane number predicted by the first octane model and a motor octane number predicted by the second octane model for each gasoline blend component utilized to produce the finished gasoline.

In some embodiments, the infrared spectroscopy comprises at least one of near infrared spectroscopy and mid-infrared spectroscopy. In some embodiments, the infrared spectrum is a near-infrared spectrum in the wavenumber range from 4000 cmto 4800 cm. In some embodiments, the infrared spectrum is a near-infrared spectrum in the wavenumber range from 5500 cmto 6000 cm.

In some embodiments, the selecting of the first subset of spectral features and the second subset of spectral features are each performed by a clustering data analysis algorithm. In some embodiments, the first blend model algorithm comprises a first regression algorithm and the second blend model algorithm comprises a second regression algorithm. In some embodiments, each regression algorithm is selected from Gaussian Process regression, Ridge regression and partial least squares regression.

In some embodiments, the first spectral database and the second spectral database each comprise near infrared spectrums obtained from at least two distinct near-infrared spectrometers.

In some embodiments, the identifying of research octane spectral features and motor octane spectral features comprises using a machine learning clustering algorithm to cluster the members of each of the first collection of liquid hydrocarbon samples and the second collection of liquid hydrocarbon samples into multiple pattern groups based upon spectral feature similarity, then adjusting the multiple pattern groups along the wavenumber axis to minimize differences between identified spectral features.

The invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings. The drawings may not be to scale. The drawings are not intended to limit the scope of the invention to the particular embodiment illustrated.

Gasoline is a complex mixture of hydrocarbons and oxygenates with variable properties, such as octane number, that form the basis of product pricing. The American Society for Testing and Materials (ASTM) standard for determining and certifying anti-knock characteristics of motor fuels utilizes standardized engines known as “knock engines” that can empirically measure both research octane number and motor octane number. However, these methods for testing octane are expensive, labor-intensive, and slow, which means they are not well-suited for directing fuel blending operations in real-time.

As an alternative, chemometric models have been developed to control fuel product octane that provide a quantitative link between chemical properties of various gasoline blend components (or subgrades) that are utilized to produce a finished gasoline and octane rating. It is common practice in commercial refineries is to maintain individual chemometric models for different gasoline “grades”, resulting in a collection of models that are tailored separately for different blending seasons. While tailoring models to specific fuel grades can drive optimal blending performance and minimize product giveaway, the task of maintaining the accuracy of such models, especially during seasonal temperature transitions, is labor intensive and sometimes requires thousands of employee hours each year. Without such maintenance, the predictive power of these multiple chemometric models deteriorates as temperatures change during the year, which increases octane giveaway.

Unfortunately, the above approach also tends to result in the existence of numerous redundant models at each refinery or blending terminal (e.g., one for each fuel product grade) given that new models may be developed for slight changes in crude oil feed compositions as well as gasoline blend component and finished product chemical composition. Utilizing a large number of models makes model maintenance tedious and more expensive, with the performance of these models prone to deteriorate over time, which increases product quality giveaway and decreases profit.

We describe herein the development of more generalized blend models that have a broader range of applicability covering many different types of gasoline blends, including multiple fuel grades. Unlike conventional schemes for producing blend models that are tailored to specific gasoline grades, the present process produces a generalized model that incorporates knowledge of both the chemical similarities in finished gasolines as well as gasoline blend components and is applicable across a wide range of octanes and blend recipes. The resulting generalized blend models simplify the task of model maintenance and provide more consistent performance over time. They also and better withstand seasonal changes to the blend requirements for finished gasolines.

In some embodiments, the process disclosed herein produces generalized blending models in part by regressing a large quantity of near infrared (NIR) spectral data obtained from analysis of both finished gasoline blends and gasoline component streams (i.e., subgrade streams) over a three-year period at a single refinery. Various chemical and mathematical linkage methods are used to generate clusters to define stream-specific models. For generalized and globalized blending models, selected finished gasoline and components deemed significant are incorporated to the clusters.

In some embodiments, the process produces globalized blending models in part by regressing NIR spectral data obtained from analysis of both finished gasoline blends and gasoline component streams at multiple refineries with the NIR spectral data obtained from each refinery by a distinct NIR spectrometers. In these embodiments, each NIR spectrometer only analyzes a portion (or subset) of the entire collection of finished gasolines and gasoline blend components obtained from all refineries. The digitized spectral data acquired for each NIR spectrum is regressed against precise knock engine measurements of the road octane number (RON) and motor octane number (MON) for each finished gasoline or gasoline component used to produce the finished gasoline. This facilitates the development of models that accurately predict either gasoline MON or gasoline RON.

As depicted in, input parameters for formulating the blend model include 1) a database comprising NIR spectral data for a collection of finished gasolines and a collection of gasoline blend components and 2) empirically measured RON and MON octane values for each member of each collection. The NIR data is pre-processed using typical data standardization methods. Next, mathematical tools such as multivariate curve resolution (MCR), classical least squares (CLS), alternative least squares (ALS), multiple linear regression (MLR) and Gaussian Process Regression are used to identify and rank the most informative features in the processed gasoline spectra that best fit the model algorithm to understand concentrations and contributions from specific components. Enabled by library searching tools, interaction coefficient effects are estimated and minimized.

Each of these regressions can be described by a linear component and a residual component, where the residual estimates represent error contributed by chemical interactions within blend components as well as error contributed by the NIR instrument itself. The optical system of each IR spectrometer utilized is aligned to the He—Ne laser frequency, the error contribution from the NIR spectrometer is likely negligible for a generalized model where a single NIR spectrometer analyzes the entire collection of finished gasolines and gasoline blend components. However, globalized models incorporate spectral data obtained from multiple NIR spectrometers and the slight differences in accuracy and precision between instruments is a more significant source of error. The residual contributed by each sample varies depending on the number of components in the model. The sample residuals are a measure of the distance between each sample and the model. The size of the residuals gives an indication about the quality of fit for the model. Under ideal modeling conditions, the residual values are within (i.e., equal to or less than) the precision of the reference knock engine tests. This served as a basis for combining component and product spectra to develop a single generalized blend model for each of RON and MON within a refinery, and in some embodiments even a single global blend model for each of RON and MON that could be used across multiple refineries.

Some embodiments comprise developing a generalized blend model that utilizes as input 1) NIR spectral data obtained via a single NIR spectrometer for a collection of gasoline blend components and finished gasolines sourced from several different source refineries, and 2) reference octane values comprising motor octane number and reference octane number derived from knock engine testing of each gasoline blend component and finished gasoline in the collection.

Some embodiments comprise developing a globalized blend model that utilizes as input data 1) NIR spectral data obtained from multiple NIR spectrometers that have analyzed at least a portion of a collection comprising gasoline blend components and finished gasolines that are sourced from multiple refineries and 2) reference octane values comprising motor octane number and reference octane number derived from knock engine testing of each gasoline blend component and finished gasoline in the collection. The globalized model may be employed across multiple refineries to blend a finished gasoline due to it being NIR spectrometer agnostic and incorporating both blend components and finished gasolines from multiple refineries at distinct geographic locations.

The collection comprising finished gasolines and gasoline blend components was collected from several geographically distinct commercial refineries. The octane range for this data set spanned 69-102 research octane number (RON) and 67-93 motor octane number (MON). Near infrared spectroscopy was utilized to analyze this collection and obtain near-infrared (NIR) spectral data, typically for wavelengths in the range from 3499 to 6000 cm, although in some embodiments, spectral data was obtained in the range from 4000 to 4800 cmusing a flat baseline starting at 4780 cm, while in other embodiments, spectral data was obtained an incorporated into the model in the range from 5500 to 6000 cm. Each NIR spectrum was represented by a finite number of digital data points that typically varies from 50-5000. This data set was pre-processed in a conventional manner comprising steps such as standardization, scaling, normalization, binarization and mean removal, as needed, and converted to wavelets coefficients data. The data were then clustered into pattern groups using machine learning data clustering techniques. In some embodiments, the clustering technique utilized was selected from partitioning based (e.g., K-means), centroid-based, density-based (e.g., density-based spatial), distribution based, hierarchical (e.g., Ward), Gaussian mixtures, and any other conventional clustering technique. The clustered data were then processed to remove data outliers using conventional techniques (e.g., Z-score) and shifted horizontally (on the wavenumber axis) as needed to minimize differences between different clusters that were attributable to differences in calibration between the multiple NIR spectrometers that contributed spectral data for the model.

The resulting clustered data were utilized to train a mathematical model for the ability to accurately predict a property (e.g., RON or MON) for gasoline blend components and finished gasolines. In some embodiments, the resulting generalized (or globalized) blending model comprised a regression model selected from: Gaussian Process, Ridge Regression and Partial Least Squares (PLS) regression. Other supervised machine learning models can optionally be utilized, based upon the prediction accuracy of the model in terms of root mean squared error (RMSE) which was preferably in the range from 0.2˜0.3 and mean absolute error (MAE), which was preferably in the range from 0.1˜0.2.

The inventive process utilizes spectral data obtained from infrared spectroscopy (IR) because this technique can capture “chemical fingerprints” of hydrocarbon samples that can be correlated with a specific property of that sample, such as octane number. In some embodiments, near-infrared (NIR) spectroscopy provides excited vibrational data indicative of the overall molecular composition of each crude oil sample. Finding spectral features that correlate with properties such as octane number are impossible to identify by examination of the spectral data alone. Thus, the complexity and subtlety of these spectral signals has been an obstacle.

Certain embodiments comprise obtaining near-infrared spectral data for a sample comprising crude oil.

Processing of raw spectral data was performed in a conventional manner, involving standardization, scaling, normalization, binarization, and mean removal, as needed. Mean removal is a technique that centers data by removing the average value of each characteristic, then scaling it by dividing non-constant characteristics by their standard deviation. This technique centers the data on zero and helps remove bias from features. The formula used to achieve this is: X=(X−mean)/std. dev. Standardization results in the rescaling of features, which in turn represents the properties of a standard normal distribution: mean=0, sd=1 In some embodiments of the globalized model, “horizontal shifting” (on the wavenumber axis) of distinct groups of clustered data was performed to minimize slight differences in the spectral data obtained from different NIR spectrometers. For these embodiments, spectral data obtained in the wavenumber range from 5500-6000 cmwas resampled into a total of 250 datapoints for further analysis, clustered into specific groups, then horizontally shifted to minimize differences between the groups that could be attributed to slight differences in measurement accuracy and precision across different NIR spectrometers utilized to analyze the data.

Some embodiments of the inventive process in part comprise mathematical transformation of the spectral data to wavelet coefficients to enhance subtle but informative features in the data. According to wavelet theory, a discrete signal such as a spectral data point can be decomposed into “approximation” and “detail” components. Wavelet packet transform (WPT) was applied to de-noise and de-convolute digitized spectral data of hydrocarbon samples by decomposing each spectrum into coefficients (wavelet coefficients) that represent the spectrum's constituent frequencies.

Wavelet coefficients offer a different approach to removal of noise from multivariate data than other techniques such as Savitzky-Golay filtering or the fast Fourier transform. Wavelets can often enhance subtle but significant spectral features to increase the general discrimination power of the modeling approach. Using wavelets, a new set of basis vectors is developed in a new pattern space that takes advantage of the local characteristics of the data. These new basis vectors are capable of better conveying the information present in the data than axes that are defined by the original measurement variables.

In some embodiments of the present inventive process, spectral signals are “decomposed” by passing each spectrum through low-pass and high-pass scaling filters to produce a low-frequency “detail” coefficient dataset and a high-frequency “approximation” coefficient dataset. The approximation coefficients correspond to the “low-frequency signal” data in the spectra, while the detail coefficients usually correspond to the “noisy signal” portion of the data. The process of decomposition was continued with different scales of the wavelet filter pair in a step-by-step fashion to separate the noisy components from the signal until the necessary level of signal decomposition was achieved. We have found that wavelet coefficients are conducive to a variety of approaches for improving the quality of the input data for training. In some embodiments, decomposition of the data using mother wavelets from the Symlet, Haar and Coiflets wavelet families facilitated the recognition of distinct spectral features in the resulting wavelet coefficients data.

Various mathematical linkage methods are used to generate clusters to define stream specific models. Enabled by library searching tools, interaction coefficient effects are estimated and minimized. Each of these models can be described by a linear component and a constant (or residual) portion. The residual portion estimates component chemical interaction and error contribution from the NIR instrument(s). Since the optical system is aligned to the He—Ne laser frequency, the contribution from a single the NIR spectrometer is negligible for the generalized model. In some embodiments, the process produces globalized blending models in part by regressing NIR spectral data obtained from analysis of both finished gasoline blends and gasoline component streams at multiple refineries utilizing multiple NIR spectrometers. In these embodiments, each NIR spectrometer has only analyzed a portion (or subset) of the entire collection of finished gasolines and gasoline blend components.

Each sample residual varies depending on the number of components in the model. The sample residuals are a measure of the distance between each sample and the model. The size of the residuals gives an indication about the misfit of the model. Modeling conditions are preferably chosen such that the residual values are within the precision of the reference knock engine tests. This serves as a basis for combining component and product spectra to develop a single model, otherwise referred to as a generalized model.

shows a flow chart outlining one embodiment of the present process. Each member of a finished gasoline collectioncomprising multiple finished gasoline blends is analyzed by near infrared spectroscopyto produce an NIR spectrum that in turn comprises spectral data, where the spectral data comprises multiple distinct digitized data points. The sum of the finished gasoline spectral dataobtained for all members of the finished gasoline collectionis then subjected to data pre-processingas described herein to produced preprocessed gasoline spectral data.

Each member of the finished gasoline collectionis also subjected to knock engine analysisto empirically derive its gasoline research octane number (RON) and collectively produce gasoline RON datafor the collection, and further, to empirically derive its gasoline motor octane number (MON) to collectively produce gasoline MON datafor the collection. The gasoline RON datais mathematically regressed against the pre-processed gasoline spectral datato produce gasoline RON regression data. The gasoline MON datais mathematically regressed against the pre-processed gasoline spectral datato produce gasoline MON regression data.

Each member of a gasoline blend component collectioncomprising multiple subgrade gasoline streams (or multiple subgrade streams) is analyzed by near infrared spectroscopyto produce an NIR spectrum that in turn comprises spectral data, where the spectral data comprises multiple distinct digitized data points. The sum of the gasoline blend component spectral dataobtained for all members of the gasoline blend component collectionis then subjected to data pre-processingas described herein to produced preprocessed blend component spectral data.

Each member of the gasoline blend component collectionis also subjected to knock engine analysisto empirically derive its blend component research octane number (RON) to collectively produce blend component RON dataand a blend component MON data (MON). The blend component RON Datais regressed against preprocessed component spectral datato produce components RON regression data. The blend component MON datais regressed against preprocessed component spectral datato produce components MON regression data.

The gasoline RON regression dataand the components RON regression dataare each curatedto select informative features within the data (i.e., regions for which the correlation with octane number is particularly strong) that are incorporated into a trained RON blend model. The gasoline MON regression dataand the components MON regression dataare each curatedto select informative features within the data (i.e., regions for which the correlation with octane number is particularly strong) that are incorporated into a trained MON blend model. The algorithms comprising the trained RON blend modeland the trained MON blend modelare each incorporated as programmingthat when executed, operates a programmable linear controllerthat is capable of implementing each blend model to produce a finished gasolinethat meets all government specifications for Anti-Knock Index (AKI) by controlling the operation of one or more adjustable valves in one or more pipes (not depicted), each pipe containing a blend component of a finished gasoline (e.g., a gasoline subgrade or subcomponent, a neat gasoline, ethanol, butane, etc). The term AKI as used herein is given its standard definition, which is the sum of (RON+MON) divided by 2.

shows a flow chart outlining one embodiment of the present process. Each member of a finished gasoline collectioncomprising multiple finished gasoline blends is analyzed by near infrared spectroscopyto produce an NIR spectrum that in turn comprises spectral data, where the spectral data comprises multiple distinct digitized data points. The sum of the finished gasoline spectral dataobtained for all members of the finished gasoline collectionis then subjected to data pre-processingas described herein to produced preprocessed gasoline spectral data.

Each member of the finished gasoline collectionis also subjected to knock engine analysisto empirically derive its gasoline research octane number (RON) and collectively produce gasoline RON datafor the collection, and further, to empirically derive its gasoline motor octane number (MON) to collectively produce gasoline MON datafor the collection. The gasoline RON datais mathematically regressed against the pre-processed gasoline spectral datato produce gasoline RON regression data. The gasoline MON datais mathematically regressed against the pre-processed gasoline spectral datato produce gasoline MON regression data.

Each member of a gasoline blend component collectioncomprising multiple subgrade gasoline streams (or multiple subgrade streams) is analyzed by near infrared spectroscopyto produce an NIR spectrum that in turn comprises spectral data, where the spectral data comprises multiple distinct digitized data points. The sum of the gasoline blend component spectral dataobtained for all members of the gasoline blend component collectionis then subjected to data pre-processingas described herein to produced preprocessed blend component spectral data.

Each member of the gasoline blend component collectionis also subjected to knock engine analysisto empirically derive its blend component research octane number (RON) to collectively produce blend component RON dataand a blend component MON data (MON). The blend component RON Datais regressed against preprocessed component spectral datato produce components RON regression data. The blend component MON datais regressed against preprocessed component spectral datato produce components MON regression data.

The gasoline RON regression dataand the components RON regression dataare each curatedto select informative features within the data (i.e., regions for which the correlation with octane number is particularly strong) that are incorporated into a trained RON blend model. The gasoline MON regression dataand the components MON regression dataare each curatedto select informative features within the data (i.e., regions for which the correlation with octane number is particularly strong) that are incorporated into a trained MON blend model. The algorithms comprising the trained RON blend modeland the trained MON blend modelare each incorporated as programmingthat when executed, operates a programmable linear controllerthat is capable of implementing each blend model to produce a finished gasolinethat meets all government specifications for Anti-Knock Index (AKI) by controlling the operation of one or more adjustable valves in one or more pipes (not depicted), each pipe containing a blend component of a finished gasoline (e.g., a gasoline subgrade or subcomponent, a neat gasoline, ethanol, butane, etc). The term AKI as used herein is given its standard definition, which is the sum of (RON+MON) divided by 2.

shows a flow chart outlining one embodiment of the present process. Each member of a finished gasoline collectioncomprising multiple finished gasoline blends is analyzed by near infrared spectroscopyto produce an NIR spectrum that in turn comprises spectral data, where the spectral data comprises multiple distinct digitized data points. The sum of the finished gasoline spectral dataobtained for all members of the finished gasoline collectionis then subjected to data pre-processingas described herein to produced preprocessed gasoline spectral data.

Each member of the finished gasoline collectionis also subjected to knock engine analysisto empirically derive its gasoline research octane number (RON) and collectively produce gasoline RON datafor the collection, and further, to empirically derive its gasoline motor octane number (MON) to collectively produce gasoline MON datafor the collection. The gasoline RON datais mathematically regressed against the pre-processed gasoline spectral datato produce gasoline RON regression data. The gasoline MON datais mathematically regressed against the pre-processed gasoline spectral datato produce gasoline MON regression data.

Each member of a gasoline blend component collectioncomprising multiple subgrade gasoline streams (or multiple subgrade streams) is analyzed by near infrared spectroscopyto produce an NIR spectrum that in turn comprises spectral data, where the spectral data comprises multiple distinct digitized data points. The sum of the gasoline blend component spectral dataobtained for all members of the gasoline blend component collectionis then subjected to data pre-processingas described herein to produced preprocessed blend component spectral data.

Each member of the gasoline blend component collectionis also subjected to knock engine analysisto empirically derive its blend component research octane number (RON) to collectively produce blend component RON dataand a blend component MON data (MON). The blend component RON Datais regressed against preprocessed component spectral datato produce components RON regression data. The blend component MON datais regressed against preprocessed component spectral datato produce components MON regression data.

The gasoline RON regression dataand the components RON regression dataare each curatedto select informative features within the data (i.e., regions for which the correlation with octane number is particularly strong) that are incorporated into a trained RON blend model. The gasoline MON regression dataand the components MON regression dataare each curatedto select informative features within the data (i.e., regions for which the correlation with octane number is particularly strong) that are incorporated into a trained MON blend model. The algorithms comprising the trained RON blend modeland the trained MON blend modelare each incorporated as programmingthat when executed, operates a programmable linear controllerthat is capable of implementing each blend model to produce a finished gasolinethat meets all government specifications for Anti-Knock Index (AKI) by controlling the operation of one or more adjustable valves in one or more pipes (not depicted), each pipe containing a blend component of a finished gasoline (e.g., a gasoline subgrade or subcomponent, a neat gasoline, ethanol, butane, etc). The term AKI as used herein is given its standard definition, which is the sum of (RON+MON) divided by 2.